9th grade · Math · Unit 18 of 19
Right-Triangle Trig
Sine, cosine and tangent
What your child practices
The three trig ratios in a right triangle (SOH CAH TOA), choosing the right ratio for the sides you know, finding a missing side, and seeing why sin A = cos B for the two acute angles.
Oregon State Standards learning standard: HS.GM.D.12; HS.GM.B.6 · using sine, cosine and tangent to find side lengths in right triangles, and the angle facts of right triangles
How we explain it
Children can open this short lesson before they practice.
- Name the sides from angle A: opposite, adjacent (next to A) and the hypotenuse (across from the right angle).
- SOH CAH TOA: sin = opposite ÷ hypotenuse, cos = adjacent ÷ hypotenuse, tan = opposite ÷ adjacent.
- Pick the ratio that uses the side you know and the side you want, then solve.
Example: sin A = 0.6 and the hypotenuse is 20 cm. How long is the side opposite A? sin A = opposite ÷ hypotenuse. opposite = 0.6 × 20. Answer: 12 cm
Sample questions
A taste of this unit. In the app, questions change every time and get easier or harder to match your child.
Question 1
A ramp rises at a 45° angle and runs 28 m along the ground. How high does it rise? (tan 45° = 1)
- 29
- 14
- 28
- 56
28
Hint: The rise is opposite the angle and the run is adjacent, so rise = run × tan 45°.
Question 2
In a right triangle, the side opposite angle A is 8, the side next to angle A is 15 and the hypotenuse is 17. What is sin A?
- 15/8
- 8/15
- 15/17
- 8/17
8/17
Hint: SOH CAH TOA: sin = opposite ÷ hypotenuse, cos = adjacent ÷ hypotenuse, tan = opposite ÷ adjacent.
Question 3
In a right triangle, cos A = 0.8 and the hypotenuse is 55 cm. How long is the side next to angle A?
- 33
- 44
- 99
- 55
44
Hint: cos A = adjacent ÷ hypotenuse, so adjacent = 0.8 × 55.
Question 4
In a right triangle, one acute angle is 35°. What is the other acute angle?
- 55°
- 145°
- 35°
- 65°
55°
Hint: The angles of a triangle add to 180°, and the right angle uses 90°, so the two acute angles add to 90°.
Question 5
For an acute angle A in a right triangle, which ratio is tan A?
- hypotenuse ÷ opposite
- opposite ÷ hypotenuse
- opposite ÷ adjacent
- adjacent ÷ opposite
opposite ÷ adjacent
Hint: Remember SOH CAH TOA: Sine is Opposite over Hypotenuse, Cosine is Adjacent over Hypotenuse, Tangent is Opposite over Adjacent.
Question 6
You know angle A and the opposite side of a right triangle. You want the adjacent side. Which ratio links them?
- Sine
- Tangent
- Cosine
Tangent
Hint: Name the two sides you are using (opposite, adjacent or hypotenuse), then find the ratio that uses exactly those two.